The classic example. Two men head toward each other, driving cars. The first to turn away is the chicken. If neither turns... well, you get the idea.
A similar scenario occurs with two guys driving their cars toward the edge of a cliff at high speed. Whichever driver stops closest to the edge of the cliff without going over wins the other driver's car. If either driver doesn't (or both drivers don't) stop in time...
Anime and Manga
Shotaro Kaneda, as the leader of the Capsules, plays chicken with the leader of the Clowns in Katsuhiro Otomo's AKIRA. This is done on a highway of Neo-Tokyo upon motorcycles at 150 kmh (88 mph).
In Calvin and Hobbes, two airplanes do this trying to land on the same runway in one of Calvin's toy-inspired fantasy sequences.
Robocop 2. During the Motorcycle Jousting between Robocop on a cycle and Cain in an armored car, the two drive straight at each other. Robocop ends up going through the armored car's windshield and grabbing Cain. Well, technically, Robocop's risk was much lower than in most cases here, but still...
This comes up in one of the first Herbie The Love Bug film. Herbie's driver chickens out but Herbie doesn't, so the driver can't turn the wheel to get out of the way of the other car.
In Rebel Without a Cause the game is to drive towards the edge of a cliff and see who will jump out first.
Invoked in Groundhog Day. Phil Connors, upon realizing he can do anything he wants with no consequences, pretends to play chicken with an oncoming train, scaring the hell out of the passengers in the car. "I'm betting he's going to swerve first."
Gattaca has a variant that brothers Vincent and Anton would play many times growing up. They both swam into the ocean, and the loser was whoever first said it was time to swim back. This was the only contest that Vincent always won (in spite of his "genetic inferiority"); at the end of the film, he explains that he won because he never saved any energy for the return trip.
Ingeniously invoked in Touchstone Pictures' Pearl Harbor, where boyhood friends Rafe McCawley and Danny Walker played chicken in propeller airplanes, learning to avoid disaster by each pilot banking hard left, turning the planes' wings almost vertical. During the fateful attack on 7 December 1941, they use this tactic while being pursued by Japanese fighters. While McCawley and Walker dodge each other successfully, their pursuers slam into each other at speed.
One of the Smokey and the Bandit movies featured the world's biggest game of chicken. It was squad cars versus diesel trucks.
The cliff variant is used in Grease2 to show how crazy one fellow is.
The final confrontation with Rosta and the main characters of Red Heat involves them going against each other with buses in a game of chicken.
A common joke is two Scottish (or whoever fits the local stereotype of that kind) betting for a small sum who will stay longer underwater. Both drown.
In Legacy of the Drow Series it is mentioned that house Oblodra has a small population because people there like playing the game with levitation spells. Two people float over the abyss. The first one to return to solid ground is the loser. More often than not, neither does.
In Isaac Asimov's Mirror Image (from The Caves of Steel series), two mathematicians aboard a starship accuse each other of stealing an important discovery. Should they make it to their destination (and therefore, an official investigation), both will have their reputations ruined. Therefore, the innocent one is as likely to admit guilt as the guilty, and the guilty is likely to admit it in such a fashion that he will look innocent. Elijah Baley actually calls it a game of intellectual chicken. The Robots of Dawn show that the entire Auroran politics work on that principle - Spacers have extreme aversion to conflict, so the whole dispute always comes to an attempt by the president to get one side to back down before it comes to blows.
In Stormbreaker, Alex plays chicken with one of Herod Sayle's mooks while riding a quadbike close to the edge of a cliff. The mook flinches first, and ends up plummeting over the cliff as a result.
In Shades of Grey, Eddie Russet reminisces on a game he and his friends used to play as children: "dusk running, where the last one back to the safety of the streetlight was the winner." (This is a world where stepping into the darkness at night can cause madness and death.) A showdown between the two champions, Lizzie and Richard, ended with Richard's complete disappearance until his body was found eight months later. The kids stopped dusk running at that point.
"What happened to Shepard?" I asked, remembering Tim Shepard's kid brother. Curly, who was a tough, cool, hard-as-nails Tim in miniature, and I had once played chicken by holding our cigarette ends against each other's fingers. We had stood there, clenching our teeth and grimacing, with sweat pouring down our faces and the smell of burning flesh making us sick, each refusing to holler, until Tim happened to stroll by. When he saw that we were really burning holes in each other he cracked our heads together, swearing to kill us both if we ever pulled a stunt like that again. I still have the scar on my forefinger. Curly was an average downtown hood, tough and not real bright, but I liked him. He could take anything.
Live Action TV
In the Doctor Who episode "The Time Monster" the Master acquires an artifact that will allow him to control an almost omnipotent transdimensional being; the Doctor initiates an overload of the Tardis's systems that will destroy them both unless the Master hands over the artifact, while the Master insists he'd rather perish than surrender absolute power. The Doctor caves first, but companion Jo triggers the overload. Fortunately they all get better.
Scrubs has Gay Chicken, where two guys lean in to kiss each other and the first one to back away loses.
In The Super Mario Bros. Super Show episode "The Toad Warrior", Kar-Krazy Koopa challenges Toad (as the Toad Warrior) to race towards a ravine. Both end up going over the edge, but while Toad is able to jump to the other side, Koopa ends up crashing into the cliff.
Five hats means that five tropers think it is ready to publish.
You are saying that you think this draft is ready to be published. That means the description is not ambiguous,
it doesn't duplicate an existing trope, there are at least three examples, and the title makes sense.
Is that what you meant to do?
You are saying this draft has a ready-to-publish hat it does not deserve and you are taking it back.